Hacking the topographic ruggedness index

The topographic ruggedness index (TRI) is widely adopted for the analysis of digital elevation models, providing information on local surface spatial variability. In this work, the TRI is interpreted according to a geostatistical perspective, highlighting its main characteristics and drawbacks. TRI can be interpreted as an omnidirectional short-range spatial variability index, computed according to a pixel centered perspective. The simplicity and interpretability of the index, free from user-dependent selections, promoted its implementation in several software environments and its application in a wide set of case studies. However, the index has several drawbacks for its application in earth sciences, such as a strong dependency on local slope (it is basically an average adjacent neighbor slope algorithm) and the selection of different lag distances in the computation of spatial variability along the main directions and the diagonal ones. We propose a new metric radial roughness (RRI) in order to solve the main drawbacks of TRI but maintaining its main philosophy (i.e., pixel centered perspective and simplicity of the algorithm). The new index corrects for the differences in lag distances and resolves the dependency on trend using increments of order 2. The code of the index, implemented in R statistical language, and test data are provided with the paper (https://doi.org/10.5281/zenodo.7132160) to promote its implementation in other software environments.